# Correlation between variables

Given n random variables x1,...,xn (one-dimensional). The following is known (corr() = Pearson correlation):

corr(x1,x2) = a
corr(x2,x3) = a


The actual values of the random variables are unkown though. Only some of their correlations are known.

From this, is it possible to calculate

corr(x3,x1) = ?


Or more generally, if the set of correlations corr(x_i, x_i+1) with i=[1..c], c<(n-1) are known, is it possible to estimate or directly calculate corr(x_1, x_c+1)?

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